Transcript Thermodynamics - Illinois State University

Thermodynamics
Temperature, Heat, Work
Heat Engines
Introduction

In mechanics (dynamics) we deal with
quantities such as mass, position, velocity,
acceleration, energy, momentum, etc.,
which describe the condition of objects.
Thermodynamics


In thermodynamics we deal with the
energy and work of a system.
We describe the system in terms of
observables which are the net result of the
mechanics quantities of all the molecules
which make up the system.
Thermodynamics
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
These observables are volume,
temperature, pressure, heat energy, work.
Thermodynamics deals with those
quantities and their relationships.
Thermodynamics deals with
what kind of quantities?
1.
2.
Macroscopic
Microscopic
50%
1
50%
2
We all know about Volume.
 Pressure:

Force
Pressure
Area
Example
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120 lb woman putting all her weight on
2 in2 of heels.
Pressure = 120 lb/2 in2 = 60 lb/in2.
Is that a lot?
Comparison: 1 atm = 14.7 lb/in2. Thus of
heals is approximately 4 atm.
This is the pressure you would feel at a
depth of approximately 135 ft of water.
Temperature and Heat
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Everyone has a qualitative understanding
of temperature, but it is not very exact.
Question: Why can you put your hand in a
400 F oven and not get instantly burned,
but if you touch the metal rack, you do?
Answer: Even though the air and the rack
are at the same temperature, they have
very different energy contents.
Construction of a Temperature Scale
Choose fixed point temperatures that are easy
to reconstruct in any lab, e.g. freezing point of
water, boiling point of water, or anything else
you can think of.
 Fahrenheit: Original idea:
0F
Freezing point of Salt/ice
100F
Body Temperature
Using this ice melts at 32F and water boils at
212F (Not overly convenient) Note: 180F
between boiling an freezing.

Celsius (Centigrade) Scale:
0C
Ice Melts
100C
Water Boils
Note a change of 1C = a change of 1.8F.

Conversion between Fahrenheit
and Celsius
If we know Celsius and want Fahrenheit
9
F  C  32
5
If we know Fahrenheitand want Celsius
5
C  F  32
9
Absolute or Kelvin Scale
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The lowest temperature on the Celsius
Scale is -273.15C.
Absolute or Kelvin Scale
Absolute or Kelvin Scale
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The lowest possible temperature on the
Celsius Scale is -273.15C.
The Kelvin Scale just takes this value and
calls it 0 Kelvins, or absolute zero.
Note: the size of 1K is the same as 1C.
To convert from C to K just add 273.15
K = C + 273.15
When do you use which scale.
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Fahrenheit: everyday use (the weather).
Use either Kelvin or Celsius when
measuring differences in temperature.
Use Kelvin when doing absolute
temperature measurements or calculating
energies or pressures
Heat
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Heat is the energy of
random motion of the
particles in the gas, i.e.
the kinetic energy of
the molecules.
Nice web simulation
gas simulation
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Temperature is a measure of the average
kinetic energy of the molecules in a body.
The higher the temperature, the faster the
particles (atoms/molecules) are moving,
i.e. more kinetic energy.
We will take heat to mean the thermal
energy in a body OR the thermal energy
transferred into/out of a body
Specific Heat
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It is easy to change the temperature of some materials
(e.g. air), hard to change the temperature of others (e.g.
water)
Specific heat c describes how much energy Q is needed to
change the temperature (T) of an body of mass m
Q
c
m T
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c is the specific heat and is a property of the
material, not a particular object.
Note: T - changes in temperature, either Kelvin
or Celsius will do.
Units of Heat
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Heat is a form of energy so we can always
use Joules.
More common in thermodynamics is the
calorie: By definition 1 calorie is the
amount of heat required to change the
temperature of 1 gram of water 1C.
1 Cal = 1 food calorie = 1000 cal.

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The English unit of heat is the Btu (British
Thermal Unit.) It is the amount of heat
required to change the temperature of 1
lb of water 1F.
Conversions:
1 cal =4.186 J
1Btu = 252 cal
Units of Specific Heat
energy
cal
J
c is
= o or
o
mass*temp change g C
kg C
Note that by definition, the specific
heat of water is 1 cal/gC.
Material
J/kgC
cal/gC
Water
4186
1
Ice
2090
0.50
Steam
2010
0.48
Silver
234
0.056
Aluminum
900
0.215
Copper
387
0.0924
Gold
129
0.0308
Iron
448
0.107
Lead
128
0.0305
Brass
380
0.092
Glass
837
0.200
Wood
1700
0.41
Ethyl Alcohol
2400
0.58
Beryllium
1830
0.436
Water has a specific heat of 1 cal/gK and iron has a
specific heat of 0.107 cal/gK. If we add equal
amounts of heat to equal masses of iron and water,
which will have the larger change in temperature?
1.
2.
3.
4.
The iron.
They will have equal
changes since the same
amount of heat is added
to each.
The water.
None of the above.
Example Calculation

Compare the amount of heat energy required to
raise the temperature of 1 kg of water and 1 kg
of iron 20 C?
 c = Q/mT  Q = cmT

Qw = (1000 g)(1 cal/gC)(20C) = 20000 cal
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QFe = (1000 g)(0.107 cal/gC)(20C) = 2140 cal
What is the increase in the temperature of
0.5 kg of aluminum when 2000 J of heat is
added (c = 900 J/kgC)?
1.
2.
3.
4.
0.95C
1.1C
2.2C
4.4C
25%
1
25%
2
25%
3
25%
4
Heat Transfer Mechanisms
1.
2.
3.
Conduction: (mostly solids) Heat transfer
without mass transfer.
Convection: (liquids/gas) Heat transfer
with mass transfer.
Radiation: By EM radiation; takes place
even in a vacuum.
Which heat transfer mechanisms
require matter?
1.
2.
3.
Conduction &
convection
Conduction &
radiation
Radiation &
convection
33%
1
33%
2
33%
3
Conduction
æ Thermal
öæ Contact öæ Temperature ö
æ Rate of ö çè Conductivity ÷øçè Area ÷øçè Difference ÷ø
ç
÷=
è Heat Flowø
( Thickness)
Conduction
Q k ADT
=
t
d
Example
Convection
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Typically very
complicated.
Very efficient way to
transfer energy.
Vortex formation is
very common feature.
liquid convection
vortex formation
Sunspot
solar simulation
Convection Examples
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Ocean Currents
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Plate tectonics
Radiation
Everything that has a temperature
radiates energy.
 Method that energy from sun reaches
the earth.
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Q
4
4
P   eAT  (const )T
t
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Note: if we double the temperature, the
power radiated goes up by 24 =16.
If we triple the temperature, the radiated
power goes up by 34=81.
A lot more about radiation when we get to
light.
Work Done by a Gas
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Work=(Force)x(distance)
=Fy
Force=(Presssure)x(Area)
W=P(Ay)
=PV
First Law of Thermodynamics
Conservation of energy

When heat is added into a system it can
either 1) change the internal energy of the
system (i.e. make it hotter) or 2) go into
doing work.
Q = W + U.
Note: For our purposes, Internal Energy is the part
of the energy that depends on Temperature.
Heat Engines
Cycle refers to closed path on a PV
diagram
 Since the system is described by
pressure and volume it is in the same
state when P and V are the same

Heat Engines
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If we can create an “engine” that
operates in a cycle, we return to our
starting point each time and therefore
have the same internal energy. Thus,
for a complete cycle
Q=W
Heat Engines
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https://www.youtube.com/watch?v=s3N_QJVucF8
Model Heat Engine
Qhot = W + Qcold
or
 Qhot – Qcold = W

(what goes in must
come out)
Efficiency
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We want to write an expression that
describes how well our heat engine works.
Qhot = energy that you pay for.
W = work done (what you want.)
Qcold = Waste energy.
Efficiency = e = W/Qhot
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If we had a perfect engine, all of the input heat
would be converted into work and the efficiency
would be 1.
The worst possible engine is one that does no
work and the efficiency would be zero.
Real engines are between 0 and 1
Qhot  Qcold
Qcold
W
e

 1
Qhot
Qhot
Qhot
Newcomen Engine
(First real steam engine)
e=0.005
Example Calculation
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In every cycle, a heat engine absorbs
1000 J from a hot reservoir at 600K, does
400 J of work and expels 600 J into a cold
reservoir at 300K. Calculate the efficiency
of the engine.
e = 400 J/1000 J = 0.4
This is actually a pretty good engine.
Example

In every cycle, a heat engine absorbs
1500 J from a hot reservoir at 500K, does
350 J of work and expels 1150 J into a
cold reservoir at 300K. Calculate the
efficiency of the engine.
The efficiency is
1.
2.
3.
e = 0.23
e = 0.3
e = 0.6
33%
1
33%
2
33%
3
Second Law of Thermodynamics
(What can actually happen)
Heat does not voluntarily flow from cold to
hot.
OR
 All heat engines have e < 1. (Not all heat
can be converted into work.)

Carnot Engine
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The very best theoretically possible heat
engine is the Carnot engine.
The efficiency of a Carnot engine depends
on the temperature of the hot and cold
reservoirs.
eCarnot
Tcold
 1
Thot
Note: T he temperatu
res must
be measuredin Kelvins!!!
Example Calculation Part II
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In every cycle, a heat engine absorbs
1000 J from a hot reservoir at 600K, does
400 J of work and expels 600 J into a cold
reservoir at 300 K. Calculate the
efficiency of the best possible engine
(Carnot efficiency).
e = 1 - 300/600 = 0.5
Recall that the actual engine has e = 0.4.
Example Carnot Efficiency

In every cycle, a heat engine absorbs
1500 J from a hot reservoir at 500K, does
350 J of work and expels 1150 J into a
cold reservoir at 300K. Calculate the
Carnot efficiency of the engine.
The efficiency is
1.
2.
3.
e = 0.23
e = 0.3
e = 0.43
33%
1
33%
2
33%
3
Laws of Thermodynamics
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Zeroth Law
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There is a game, and you’re in it
Laws of Thermodynamics
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Zeroth Law
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There is a game, and you’re in it
First Law
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You can’t win
Laws of Thermodynamics
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Zeroth Law
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First Law
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There is a game, and you’re in it
You can’t win
Second Law
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You can’t break even
Laws of Thermodynamics
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Zeroth Law
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First Law
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You can’t win
Second Law
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There is a game, and you’re in it
You can’t break even
Third Law
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You can’t get out of the game